1. Field of the Invention
The present invention relates, in general, to a method of estimating the parameters of time series data using a Fourier transform and, more particularly, to a method of estimating the parameters of time series data using a Fourier transform, which can shorten the time required for calculation.
2. Description of the Related Art
Generally, mode (eigenvalue) analysis using eigenanalysis is widely applied to the analysis of a dynamic system. However, since eigenanalysis cannot be directly applied to time series data, only frequency analysis is restrictively applied to time series data.
For a method of estimating a mode in time series data, a Prony method has been generally used. However, this method calculates a complex exponential function on the basis of a linear prediction matrix obtained by converting signals into an autoregressive moving average (ARMA) model.
A Prony method is problematic in that, since a linear prediction equation must be solved and the solution of a higher order equation must be calculated when signals are fitted to a complex exponential function, the time required for calculation increases. This method entails noise error, and a mode sensitively varies with an interval between signal data and the intensity of the data.
Recently, Fourier transforms have been broadly applied to various industrial fields. Especially, with the development of a fast Fourier transform (FFT), Fourier transforms have been used to detect and analyze the frequency of a given signal using a computer.
Fast Fourier transforms have been mainly used to precisely and rapidly obtain the frequency of a given signal. In a dynamic system, a real part of a mode used to learn damping characteristics is a more important factor than the frequency of the mode.
For a technique of estimating a real part using a Fourier transform, only a sliding window method of FIG. 1 of repeatedly calculating the attenuation level of the magnitude of a Fourier spectrum to estimate a mode has been developed.
In FIG. 1, a signal x(t) is Fourier transformed over equal time intervals (a), (b) and (c) to calculate respective spectrums. The sliding window method is a method of estimating the real part of a mode by fitting the peak values of the spectrums to an exponentially damped function.
However, the conventional method is problematic in that a Fourier transform must be repeatedly calculated depending on a computer simulation, thus increasing the time required for calculation.